A topology optimization method based on the multiple phase projection method (a new formulation of the projection function for reducing the number of design variables

Abstract

The topology optimization method is the most flexible optimization method that allows both shape and topological changes during the optimization process. However, due to its high flexibility, the utility of topology optimization results is ofien spoiled by a preponderance of impractical designs that are difficult or impossible to manufacture, such as stmctures with numerous extremely thill members aild tiny holes. This paper proposes a new structural optimization methodology that reduces the number of design variables in a multiple phase projection method, which advantageously reduces computational time and benefits mantifacturability. The multiple phase projection method is a geometrical contraint method that imposes a minimum length scale Oil both solid aild void phases. Normally, two desigil variables are associated with each of these phases at each node in the finite element analysis, itsulting in an undesirable increase in the number of desigil variables. To mitigate this problem, we develop a new methodology that requires oilly one design variable at each node. An optimum design example for a minimum compliance problem is provided to confirm that the new methodology provides reasonable solutiolls that achieve the giveil mrnimum leilgth scale usiilg a reduced niumber of desigil variables. © 2011 The Japan Society of Mechanical Engineers.